What is QED?

Our Name

Our name, QED (Quantitative Engineering Design), is a play on the Latin phrase quod erat demonstrandum, which translates to “that which was to be demonstrated.” Mathematicians and philosophers dating from antiquity through the Renaissance would write this phrase at the end of written arguments, to indicate they had successfully proven what they set out to prove. This is the end-state we wish to achieve when solving meaningful problems.

The written representation of this concept has evolved over time. Initially it was written out fully, as shown in Euclid’s Elements. Later it was abbreviated as “Q.E.D.”, as illustrated in Spinoza’s Ethics. Today, in modern mathematical papers typeset with Knuth’s LaTeX, this initialism is further abbreviated as simply a square (Unicode U+25A2): ▢.

quod erat demonstrandum
Euclid’s Elements
Spinoza's Ethics
square Unicode U+25A2

Our Logo

Following this theme, our logo is also shaped like a square. The style of the square comes from the I Ching (易经), or “Book of Changes”. We now provide some historical background about this text.

The I Ching is the oldest of the Chinese classics, dating back to 1000 BC. Originally it was used as an oracle by kings to predict the future. Over time, it became a general guide for moral decision making, used to organize governments, root out corruption, and provide the foundations of Confucianism, Taoism, and Tai Chi.

The core of the I Ching lies in its system of hexagrams, which consists of six horizontal bars stacked together, each of which can be either open (Yin) or closed (Yang). By varying the pattern of open and closed, sixty-four different hexagrams can be created, as illustrated below in their original ordering. Each hexagram is associated with a different phenomenon, such as #46: 升 (Pushing Upward / Ascending), or #7: 师 (The Army / Leading).

During the Song dynasty, a philosopher named Shao Yong (邵雍, 1011–1077 AD) provided a novel reordering of these hexagrams, shown as follows:

This arrangement should look familiar to anyone involved with computation or mathematics … it is the binary number system! By interpreting Yin as 0 and Yang as 1, every hexagram is mapped to a 6-bit integer, between 0 and 63 inclusive. In fact, the I Ching provided Leibniz with the inspiration to bring binary to the West.

Another figure in Chinese history, King Wen of Zhou (周文王, 1099–1050 BC), observed that by flipping a hexagram upside down, we can generate another hexagram that is referred to as its dual. Consequently, by drawing vertical strikes rather than horizontal ones, King Wen compressed 64 hexagrams into 32 dualities.

The duality we chose for our logo is the following:

Left-hand side (rotate -90°):

Character: 革 (gé) = revolution

Binary Index: 101110 = 2^0 + 2^2 + 2^3 + 2^4 = 29

Etymology: Picture of a dead animal’s skin being flayed from its hide.

Interpretation: “Abolishing the Old.”

Right-hand side (rotate +90°):

Character: 鼎 (dǐng) = cauldron

Binary Index: 011101 = 2^1 + 2^2 + 2^3 + 2^5 = 46

Etymology: Picture of an ancient cooking vessel.

Interpretation: “Establishing the New.”

The Message

Putting the hexagrams together, this is the message embedded within: to abolish the old and establish the new.

Humans go through life searching for constants and consistencies to believe in, only to eventually discover that no such things exist. In both the East and the West, our ancestors knew this and advised posterity to embrace uncertainty and explore the unknown.

“The only thing that is constant is change.” – Heraclitus

“Impermanent are all created things; Strive on with awareness.” – Buddha

“Whosoever desires constant success must change his conduct with the times.” – Machiavelli

“Everything flows on and on like this river, without pause, day and night.” – Confucius

“The important thing is to not stop questioning.” – Einstein

We accept disruption as a necessity for the betterment of humanity. To build better solutions, we cannot be afraid to break away from popular conventions, even at the risk of inconvenience or ostracism, because the will to break away is the catalyst of all scientific progress. We free ourselves from the confines of pre-existing notions about how an efficient workforce or research operation must or must not be structured, which nations or peoples we should or should not work with, or what others say we can or cannot do. This is the ideal underlying QED, to embrace the cycle of disruption that is the source of all innovation and provides optimism toward building a future more livable for all people.

– William Wu, 2016-06-25